James W. Brennan

All the basic operations of arithmetic can be defined in terms of addition,
so we will take it as understood that you have a concept of what addition
means, at least when we are talking about positive numbers.

A positive number represents a
distance to the right on the number line, starting from zero (zero is also
called the origin since it is the starting point). When we add another
positive number, we visualize it as taking another step to the right by that
amount. For example, we all know that 2 + 3 = 5. On the
number line we would imagine that we start at zero, take two steps to the
right, and then take three more steps to the right, which causes us to land on
positive 5.

What does it mean to add
negative numbers? We view a negative number as a displacement to the left on
the number line, so we follow the same procedure as before but when we add a
negative number we take that many steps to the left instead of the right.

Examples:

2 + (–3) = –1

First we move two steps to the
right, and then three steps to the left:

(–2) + 3 = 1

We move two steps to the left,
and then three steps to the right:

(–2) + (–3) = –5

Two steps to the left, and then
three more steps to the left:

From these examples, we can
make the following observations:

1.If we add two positive numbers together, the result will be
positive

2.If we add two negative numbers together, the result will be
negative

3.If we add a positive and a negative number together, the
result could be positive or negative, depending on which number represents the
biggest step.